1 Getting Started

1.7 The statistical forecasting perspective

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

Random futures

A forecast is an estimate of the probabilities of possible futures.

“He who sees the past as surprise-free is bound to have a future full of surprises.” (Amos Tversky)

Statistical forecasting

  • Thing to be forecast: a random variable, y_t.
  • Forecast distribution: If {\cal I} is all observations, then y_{t} |{\cal I} means “the random variable y_{t} given what we know in {\cal I}.
  • The “point forecast” is the mean (or median) of y_{t} |{\cal I}
  • The “forecast variance” is \text{var}[y_{t} |{\cal I}]
  • A prediction interval or “interval forecast” is a range of values of y_t with high probability.
  • With time series, {y}_{t|t-1} = y_t | \{y_1,y_2,\dots,y_{t-1}\}.
  • \hat{y}_{T+h|T} =\text{E}[y_{T+h} | y_1,\dots,y_T] (an h-step forecast taking account of all observations up to time T).